MalthusandSolow(中级宏观经济学,香港中文大学).pptx

MalthusandSolow(中级宏观经济学,香港中文大学).pptx

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Chapter6,EconomicGrowth:

MalthusandSolow,TheMalthusianModelofEconomicGrowth,Malthusargued:

advancesinthetechnologyforproducingfoodincreasedpopulationgrowthnoincreaseinthestandardoflivingunlessthereweresomelimitsonpopulationgrowthAdynamicmodelwithmanyperiodsConfineattentiontowhathappensinthecurrentperiodandthefutureperiod,Aggregateproductionfunctionwithconstantreturnstoscale:

（1）whereiscurrentaggregateoutputiscurrentfixedsupplyoflandiscurrentlaborThereisnoinvestmentandnogovernmentspendingAssumeeachpersoniswillingtoworkatanywageandhasoneunitoflabortosupply（anormalization）,sothatinEquation

（1）,isboththepopulationandthelaborinput,Supposepopulationgrowthdependsonthequantityofconsumptionperworker

（2）whereisthepopulationinthefuture（next）periodisanincreasingfunctionisaggregateconsumptionsothatiscurrentconsumptionperworker,mainlyduetothefactthathigherfoodconsumptionperworkerreducesdeathratesthroughbetternutrition,Allgoodsproducedareconsumed,soC=Y.Hence,（3）ThenuseEquation（3）tosubstituteforCinEquation

（2）:

（4）Theconstant-returns-to-scalepropertyoftheproductionfunctionimpliesthatAftermultiplyingeachsidebyN,Equation（4）canberewrittenas（5）,PopulationgrowthdependsonconsumptionperworkerintheMalthusianmodelisthesteadystateforthepopulationIfthenpopulationincreasesIfthenpopulationdecreases,SteadyStateAnalysisoftheMalthusianModel,RecallLetting,andThenfromEquation

（2）:

Inthesteadystate,sothencanbedetermined,Inpanel（b）,isdeterminedInpanel（a）,isdeterminedfromtheper-workerproductionfunctionSteadystatepopulationisgivenby,TheSteadyStateEffectsofanIncreaseinz,Supposetheeconomyisinitiallyinasteadystate,with,whichthenincreasesonceandforalltimetounchangedfallsSteadystatepopulationincreases,PopulationincreasesovertimetoitssteadystatevalueincreasesattimeTconsumptionperworkerincreasesthendeclinetoitssteadystatevalueAnotherexample:

populationcontrolbothc*andl*increase.,HowUsefulistheMalthusianModelofEconomicGrowth?

BeforetheIndustrialRevolutioninabout1800:

economicgrowthconsistentwiththeMalthusianModelFromtheperspectiveoftheearly21stcentury:

MalthuswaswrongWhy?

-Didnotallowfortheeffectofincreasesinthecapitalstockonproduction,and-Didnotaccountforalltheeffectsofeconomicforcesonpopulationgrowth,TheSolowModel:

ExogenousGrowth,Consumers:

Thepopulationgrowsovertime:

whereisthepopulationinthefutureperiodistherateofgrowthinthepopulationAssumethatconsumersconsumeaconstantfractionofincomeineachperiod:

whereiscurrentconsumptionistheaggregatesavingsrate,TheRepresentativeFirm:

Constantreturnsproductionfunctionwithcapitalandlaborinputs:

whereisoutputperworkeriscapitalperworkerwhereisconstantdepreciationrateand,CompetitiveEquilibrium:

Equilibriumcondition:

Quantityofcapitalperworkerconvergestoaconstant,quantityofoutputperworkerconvergestoaconstant,Ifs,nandzareconstant,realincomeperworkercannotgrownobettermentinlivingstandards,SteadyStateAnalysis,Inthelongrun,whentheeconomyconvergestothesteadystatequantityofcapitalperworker,k*,allaggregatequantities（K,Y,IandC）growattheraten.,AnalysisoftheSteadyState,Inthesteadystate,byrearranging,ComparativeStatics:

AnIncreaseintheSavingsRate,Thecurve,shiftsuplevelsofcapitalperworkerandoutputperworkerarehigherBUTthereisnoeffectonthegrowthratesofaggregatevariables,BeforetimeT,aggregateoutputisgrowingattheconstantrate,SavingsrateincreasesattimeTAftertimeT,outputthenconvergesinthelongruntoanewhighersteadystategrowthpath,ConsumptionperWorkerandGoldenRuleCapitalAccumulation,Consumptionperworkerinthesteadystateis（goldenrulequantityofcapitalperworker）givesthemaximumconsumptionperworker,Propertyofthegoldenrule:

ComparativeStatics:

AnIncreaseinLaborForceGrowth,Anincreaseinthelaborforcegrowthrate（n）causesadecreaseinthequantityofcapitalperworkerandoutputperworkerGrowthratesinaggregateoutput,aggregateconsumptionandaggregateinvestmentincrease,ComparativeStatics:

AnIncreaseinTotalFactorProductivity,TheSolowModelpredictsthatacountrysstandardoflivingcancontinuetoincreaseinthelongrunonlyiftherearecontinuingincreasesintotalfactorproductivity（z）,MathematicalSolution（Appendixp.636）,Inthesteadystate,Hence,Thesignisambiguous,sothatconsumptionperworkercouldincreaseordecreasewithanincreaseinthesavingsrate,ThegoldenrulesteadystatequantityofcapitalperworkersolvestheproblemsolvesorAs,Recallinthesteadystate,TotallydifferentiatingEquation（A.1）,wegetHence,solvingfortheappropriatederivatives,GrowthAccounting,Ifaggregaterealoutputistogrowovertime,itisnecessaryforafactororfactorsofproductiontobeincreasingovertime,orfortheretobeincreasesintotalfactorproductivity.GrowthAccounting:

anexercisetomeasurehowmuchofthegrowthinaggregateoutputoveraperiodoftimeisaccountedforbygrowthineachoftheinputstoproductionandbyincreasesintotalfactorproductivity,GrowthAccounting,GrowthaccountingstartsbyconsideringtheaggregateproductionfunctionfromtheSolowgrowthmodel,Cobb-Douglasproductionfunctionisagoodanalyticaltoolforgrowthaccounting.Theproductionfunctiontakestheformwhere,GrowthAccounting,Supposeweset=0.36,thentheproductionfunctionisIfwehavemeasuresofaggregateoutput,thecapitalinput,andthelaborinput,thentotalfactorproductivitycanbemeasuredasaresidual,AGrowthAccountingExercise,Thetableshowshowthegrowthinthecapitalstock,inemployment,andintotalfactorproductivitycontributetothegrowthinrealoutput,Increasesinmeasuredtotalfactorproductivitycouldbetheresultof:

-newinventories-goodweather-newmanagementtechniques-favorablechangesingovernmentregulations-decreasesintherelativepriceofenergy（anyotherfactorthatcausesmoreaggregateoutputtobeproducedgiventhesamequantitiesofaggregatefactorinputs）,SolowResidualsandtheProductivitySlowdown,Totalfactorproductivitywasveryhighthroughoutmostofthe1950sand1960sDramaticdecreaseintotalfactorproductivitygrowthbeginninginthelate1960sandcontinuingintothe1980s:

productivityslowdown,SomeReasonsfortheProductivitySlowdown,MeasurementProblem:

manufacturinggoodsservicesIncreasesintherelativepriceofenergy:

measurementproblemininputs3.Thecostsofadoptingnewtechnology:

informationrevolutionandlearning,TheCyclicalPropertiesofSolowResiduals,FluctuationsinSolowresidualsabouttrendarehighlypositivelycorrelatedwiththefluctuationsinGDPabouttrendFluctuationsintotalfactorproductivitycouldbeanimportantexplanationforwhyGDPfluctuates（RBCtheory）,